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Acquisitions and Divestitures - Additional Information (Detail) - USD ($)
$ in Millions
1 Months Ended 6 Months Ended
Apr. 30, 2021
Mar. 31, 2021
Mar. 31, 2020
Acquisitions And Divestitures [Line Items]      
Cash paid for business acquisition   $ 10 $ 58
Goodwill, Acquired During Period   13  
Business divestitures, net of cash divested   19 0
Goodwill, Written off Related to Sale of Business Unit   6  
Building Solutions EMEA/LA      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   13  
Goodwill, Written off Related to Sale of Business Unit   0  
Building Solutions Asia Pacific      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   0  
Goodwill, Written off Related to Sale of Business Unit   6  
Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   0  
Goodwill, Written off Related to Sale of Business Unit   0  
Business Divestitures, Not Specific | Building Solutions Asia Pacific      
Acquisitions And Divestitures [Line Items]      
Proceeds from Divestiture of Businesses   23  
Business divestitures, net of cash divested   19  
Goodwill, Written off Related to Sale of Business Unit   6  
Individually Immaterial Acquisitions      
Acquisitions And Divestitures [Line Items]      
Purchase price, net of cash acquired   15 61
Cash paid for business acquisition   10 58
Individually Immaterial Acquisitions | Building Solutions EMEA/LA      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period   $ 13 20
Individually Immaterial Acquisitions | Global Products      
Acquisitions And Divestitures [Line Items]      
Goodwill, Acquired During Period     $ 19
Subsequent Event [Member] | Silent-Aire      
Acquisitions And Divestitures [Line Items]      
Purchase price, net of cash acquired $ 870    
Cash paid for business acquisition $ 630